Problem: Solve for $x$ : $6\sqrt{x} - 6 = 9\sqrt{x} + 9$
Solution: Subtract $6\sqrt{x}$ from both sides: $(6\sqrt{x} - 6) - 6\sqrt{x} = (9\sqrt{x} + 9) - 6\sqrt{x}$ $-6 = 3\sqrt{x} + 9$ Subtract $9$ from both sides: $-6 - 9 = (3\sqrt{x} + 9) - 9$ $-15 = 3\sqrt{x}$ Divide both sides by $3$ $\frac{-15}{3} = \frac{3\sqrt{x}}{3}$ Simplify. $-5 = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.